01 - Preheat oven to 350°F and line two baking sheets with parchment paper.
02 - In a medium bowl, whisk together flour, matcha powder, baking powder, and salt until well blended.
03 - In a large bowl, beat butter and sugar with an electric mixer on medium-high speed until light and fluffy, approximately 2 to 3 minutes.
04 - Add egg and vanilla extract to the butter mixture, mixing until thoroughly combined and smooth.
05 - Gradually add the dry ingredient mixture to the wet ingredients, mixing on low speed just until incorporated and no dry streaks remain.
06 - Scoop tablespoon-size portions of dough and roll into balls. Place on prepared baking sheets, spacing 2 inches apart to allow for spreading.
07 - Gently flatten each dough ball with your palm or the bottom of a glass to create even cookie rounds.
08 - Bake for 10 to 12 minutes, until edges are set but centers remain slightly soft. Allow cookies to cool on baking sheets for 3 minutes, then transfer to a wire rack to cool completely.
09 - Beat butter until creamy and smooth. Gradually add powdered sugar, mixing well after each addition. Incorporate milk, ground lavender, vanilla extract, and salt. Continue beating until light and fluffy. Add purple gel food coloring if desired and mix to combine.
10 - Once cookies have cooled completely, spread a generous layer of lavender buttercream over each cookie. Garnish with a pinch of culinary lavender buds for an elegant finish.